History of Numerals and Symbols

Date: 06/22/98 at 21:50:49
From: Melanie Edgar
Subject: Symbol history
We originally used the Roman system of nurmerals but the current
symbols originated from the Hindo-Arabic system of numerals. Why and
when did this change ocour?
The symbols + and - have been commonly used in arithmetic texts since
the 15th century. Can you tell us the history of symbols like =,
divided by, times, etc.?
Thank you.

Date: 06/23/98 at 12:58:13
From: Doctor Mateo
Subject: Re: Symbol history
Hello Melanie,
You ask some very interesting questions here.
Actually there were many numeral systems in existence even before the
Roman system of numerals to which you refer. The Hindu-Arabic symbols
have themselves changed over the centuries into what we use today.
The change on the European continent to the Hindu-Arabic system took a
very long time. The Spanish used Hindu-Arabic symbols in writing as
early as the late 900s A.D.
The spread of the Hindu-Arabic numerals into standard usage took a
long time especially in Italy, where the Roman numeral system was
dominant until the middle of the 16th century A.D. In some places in
Italy it was forbidden to use anything but Roman numerals in the late
1200s and early 1300s.
When did the big change or acceptance of the Hindu-Arabic numeral
system take place? Probably during the mid-1500s. Why? Because the
printing press came into existence in the mid-1400s and the Hindu-
Arabic numerals were used in printing. By the middle of the 16th
century (and even later in some of the conservative parts of Italy)
most of Europe had accepted Hindu-Arabic numerals.
Why use Hindu-Arabic numerals instead of the Roman numerals? The
transition happened after the printing press standardized the way the
Hindu-Arabic numerals looked, but basically it was an issue of making
good use of individuals' time. It took merchants and bookkeepers much
longer to record data using Roman numerals. The Hindu-Arabic numerals
made keeping records less time-consuming.
The + and the - sign were originally used to show surpluses and
deficits in business dealings. Johann Widmann used them in his book
Mercantile Arithmetic; the book was published in 1489. The Dutch
mathematician Vander Hoecke was the first person known to use the
+ and - symbols in writing algebraic expressions (early 1500s).
The = symbol was introduced by Robert Recorde in his book The
Whetstone of Witte in 1557. The first = symbol was made with much
longer lines. The = symbol was chosen by Recorde because he felt that
there was nothing more equal than two straight parallel lines.
The multiplication symbol took a lot longer to develop. In the early
1600s Thomas Harriot used the dot to indicate multiplication in his
book _Artis Analyticae_ (1631), and William Oughtred used the x as a
symbol for multiplication in his book _Clavis Mathematicae_ (1631).
The division symbol / was introduced into written form in 1659 by
Johann Heinrich Rahn. He first used this symbol for division in his
book _Teutsche Algebra_. (This division symbol was sometimes used for
subtraction until symbols started becoming standardized.)
The symbols were introduced to make writing faster and easier, to take
up less written space, and to help the printing process.
A good resource for learning more about the history of numbers and
symbols is David M. Burton's _The History of Mathematics: An
Introduction_. On the Web, consult "Earliest Uses of Mathematical
Symbols" by Jeff Miller et al.:
http://jeff560.tripod.com/mathsym.html
Hope this helps you appreciate the development of mathematics as we
know it today just a little more.
-Doctors Mateo and Sarah, The Math Forum
http://mathforum.org/dr.math/